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1、10姓名学号学院专业座位号(密封线内不答题)……………………………………………………密………………………………………………封………………………………………线……………………………………线………………………………………_____________________…诚信应考,考试作弊将带来严重后果！华南理工大学期末考试《概率统计（双语）》试卷B2009－2010学年度下学期注意事项：1.考前请将密封线内各项信息填写清楚；2.所有答案请直接答在试卷上。3．考试形式：闭卷；满分：100分4．考试时间120分钟。题号123总分分值256015得分评卷人1．FILLINGTHEBLANKS(25poin
2、ts)(1)Inabagtherearemwhiteballsandnblackballs.Ifwedrawoneballfromthebag,theprobabilityoftheballbeingawhiteoneis.IftherearethreepersonA,B,C.Adrawaballatfirst,thenBdrawaball,thenCdrawtheball,iftheydon’tputtheballbackintothebag,theprobabilityforCtodrawawhiteballism/(m+n).(2)Iftheprobabilitydensityofa
3、randomvariableXisgivenby,3,theprobabilityforXtotakeavaluebetween0.5and1.5is7/8.《》试卷第10页共10页10(3)SupposeD(X)=36,D(X-Y)=62,D(X+Y)=42.____-5/24.(4)Ifarandomvariablehasmeanandstandarddeviation,Chebyshev’stheoremtellusthat.(5)Ifwehaveanormalsampleofsizen(nissmall)withsamplemeanandsamplevariance.Wewillr
4、ejectthehypothesiswithsignicantlevelif.(6)Supposethepairisindependent,havetheuniformdistributionintheinterval.=__________.(7)Letbeavariablefollowinganexponentialdistributionwithvariance,thedensityfunctionofis.(8)Let,andareindependent,isan-distributionwithdegreeand,i.e..2.COMPUTATIONS:(60points)《》试
5、卷第10页共10页10(1).Thereare4whiteballs,6blackballsinabag.Aballisdrawnatrandomfromthebagandtwoballsofanothercoloristhenputintothebag.Thenasecondballisdrawn.Ifthetwoballsdrawnareofthesamecolor,whatistheprobabilitythattheyarebothblack?Solution:setandastheeventsofthetwoballsareallblack,white,andofthesamec
6、olor,respectively.Then,Thustheprobabilityis(2).Asupermarketisdoinganadcompaignbyorganizingaluckyraffledrawforevery100purchasers.Therulesisthateveryonewritehisownnameonacard,putthecardintoalotterybox,thusthereare100namesinthebox.Noweveryonedrawacardfromtheboxwithoutreplacement,onebyone.Theonewhodra
7、wthecardwithhisownnamegeta50%discountonthepurchasing.Whatistheprobabilitythatnoonewillgetthediscount?(Assumethatthe100purchasershavedifferentnames.)Solution:Numberthepurchaserfrom1to100.Denoteastheeventsofnumberg
